Is it possible to reroll champion shards into a champion I already own?
I've rerolled two sets of three champion shards and both times I've managed to get a champion I don't yet own, despite only having ~20 unowned champions.
So is it possible to reroll 3 shards into a champion you own? What happens when you own all the champions?
No, this is not possible. You'll always get a champion permanent of a champion that you do not have unlocked.
As Riley said, you'll always get a champion that you don't have unlocked yet by this way. (I have every champions, and I unlock the last 2 champions by this way)
If you have all the champions and try to reroll three champions, you will get a shard and you will be able to reroll it again (so you lost 2 shards).